本文選題：非傅里葉導(dǎo)熱　切入點：傳遞矩陣法　出處：《北京交通大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：在急速傳熱的系統(tǒng)中,由于時間尺度或空間尺度及其微小,這使得傅里葉導(dǎo)熱定律在這些極端條件下不在適用。且傅里葉導(dǎo)熱定律暗含的假設(shè)是熱量傳播的速度是無窮大。因此,為了解決上述問題,Cattaneo和Vernotte對傅里葉導(dǎo)熱定律進(jìn)行了修正提出了非傅里葉導(dǎo)熱的單相弛豫模型(Cattaneo-Vernotte模型,CV模型)。CV模型的引入,使得傳統(tǒng)的溫度擴散方程轉(zhuǎn)化為一個雙曲的波動方程,即熱波波動方程。CV模型暗含的假設(shè)為熱流產(chǎn)生的溫度梯度的傳播速度為無窮大,這顯然不符合實際,為了解決這一問題,Tzou于1995年提出了雙相弛豫模型(Dual Phase Lag模型,DPL模型)。若熱量是以波的形式傳播,就不得不提在經(jīng)典波(電磁波、彈性波、聲波、格波等)領(lǐng)域,抑或是非經(jīng)典波領(lǐng)域(de Broglie波)領(lǐng)域,一個極端重要而又極具挑戰(zhàn)性的問題,波的調(diào)控。借助于光子晶體、聲子晶體的研究,本文從波的調(diào)控角度入手,提出一種可以調(diào)控?zé)崃總鞑バ袨榈娜斯ぶ芷诮Y(jié)構(gòu)-熱波晶體。分別基于CV和DPL模型,利用傳遞矩陣法、時域有限差分方法研究一維熱波晶體中的非傅里葉導(dǎo)熱問題。計算了熱波在其中傳播時的頻散曲線,初步探討了熱波晶體控制熱量傳播行為的機理,并分析了結(jié)構(gòu)參數(shù)、材料參數(shù)對熱波能帶結(jié)構(gòu)的影響。為了能夠?qū)⒗碚摻Y(jié)果應(yīng)用于實際,本文將實際生活中常見的界面熱阻引入熱波晶體,并分析了其影響。主要的研究結(jié)果表明:1、影響帶隙的結(jié)構(gòu)參數(shù)和材料參數(shù)為填充率、無量綱長度、導(dǎo)熱率比、體積熱比、弛豫時間比。其中,導(dǎo)熱率比和弛豫時間比為控制帶隙產(chǎn)生的主要參數(shù),兩者為一定值時帶隙接近消失。除無量綱長度結(jié)構(gòu)外,其他的參數(shù)和材料均能影響帶隙內(nèi)熱波的衰減速度,其中對衰減速度最大的為弛豫時間比、體積熱比。2、用以表示結(jié)構(gòu)尺寸和聲子自由程的無量綱長度和導(dǎo)熱率比成為控制帶隙頻率范圍高低的主要因素,其中如果無量綱長度過大即結(jié)構(gòu)尺寸遠(yuǎn)遠(yuǎn)大于聲子自由程時,帶隙被淹沒。3、界面熱阻會使熱波衰減更快,且令CV模型和DPL模型頻散曲線趨近一致。基于傅里葉定律的熱阻會在低頻率處增加一條帶隙。
[Abstract]:In a system of rapid heat transfer, due to the small scale of time or space, This makes the Fourier law of heat conduction not applicable under these extreme conditions, and the implicit assumption of the law of Fourier heat conduction is that the speed of heat propagation is infinite. In order to solve the above problems, Cattaneo and Vernotte have modified the Fourier heat conduction law. The introduction of Cattaneo-Vernotte model and CV model makes the traditional temperature diffusion equation transform into a hyperbolic wave equation. That is, the thermal wave wave equation .CV model implies that the temperature gradient generated by the heat flux is infinitely fast, which is obviously not in line with the reality. In order to solve this problem, Tzou put forward the dual Phase Lag model in 1995. If the heat is propagated in the form of waves, it has to be mentioned in the field of classical waves (electromagnetic wave, elastic wave, acoustic wave, lattice wave, etc.). Or in the field of nonclassical wave field de Broglie wave, a very important and challenging problem, wave regulation. With the help of the study of photonic crystal and phonon crystal, this paper starts from the angle of wave regulation. A kind of artificial periodic structure-thermal wave crystal, which can regulate the heat transfer behavior, is proposed, based on CV and DPL models, the transfer matrix method is used. The finite difference time-domain (FDTD) method is used to study the non-Fourier heat conduction in one-dimensional thermal wave crystals. The dispersion curves of the thermal waves propagating in the crystals are calculated, the mechanism of controlling the heat propagation behavior of the thermal wave crystals is preliminarily discussed, and the structural parameters are analyzed. The influence of material parameters on the structure of the thermal wave band. In order to apply the theoretical results to the practical application, the common interface thermal resistance in real life is introduced into the thermal wave crystal in this paper. The main results show that the structural and material parameters affecting the band gap are filling ratio, dimensionless length, thermal conductivity ratio, volumetric heat ratio, relaxation time ratio. The ratio of thermal conductivity and relaxation time are the main parameters to control the generation of band gap. The band gap is nearly disappeared when they are two values. Except for dimensionless length structure, other parameters and materials can affect the attenuation rate of thermal wave in band gap. The biggest attenuation velocity is relaxation time ratio and volume-heat ratio, which is used to express the dimensionless length and the thermal conductivity ratio of the structure size and the free path of phonon, which are the main factors controlling the frequency range of band gap. If the dimensionless length is too large, the structure size is much larger than the free path of the phonon, the band gap is submerged. 3, the thermal resistance of the interface will make the thermal wave decay faster. The dispersion curves of CV model and DPL model are consistent. The thermal resistance based on Fourier law increases a band gap at low frequency.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O736

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 于海燕;張昊春;魏衍強;李W，

本文編號：1598709